Problem: Solve for $x$ and $y$ using elimination. ${-4x+3y = -8}$ ${5x-3y = 13}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-4x+3y = -8}\thinspace$ to find $y$ ${-4}{(5)}{ + 3y = -8}$ $-20+3y = -8$ $-20{+20} + 3y = -8{+20}$ $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ You can also plug ${x = 5}$ into $\thinspace {5x-3y = 13}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ - 3y = 13}$ ${y = 4}$